"Even though the reasons for naturalisation applications are not collected statistically, for us there is a clear connection" to the referendum to leave the EU, a Hamburg city spokesman said.
Darmstadt's regional government, which has Frankfurt and Wiesbaden within its borders, received 521 applications in 2016 following the Brexit vote - five times more than the total for the previous year.
It was a similar story in the southwest state of Baden-Württemberg, with 386 applications last year and 68 in 2015.
Figures for the whole of Germany have still to be released.
Earlier this year the Irish Foreign ministry reported that there had been a 40 per cent rise in nationality applications from Britons following the Brexit vote.
Other EU countries also reported a sharp rise in applications and inquiries including Poland, where anybody with one Polish parent is entitled to apply for a passport.